Abstract
We compute the number of order-preserving and -reversing maps between posets in the class of fences (zig-zags) and crowns (cycles).
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Currie, J. D. and Visentin, T. I. (1991) The number of order-preserving maps of fences and crowns,Order 8, 133–142.
Duffus, D., Rödl, V., Sands, B., and Woodrow, R. (1992) Enumeration of order preserving maps,Order 9, 15–29.
Farley, J. D. (1992)Order-Preserving Maps between Posets in the Class of Crowns, Fences, and Chains, unpublished.
Goldberg, S. (1958)Introduction to Difference Equations with Illustrative Examples from Economics, Psychology, and Sociology, Wiley, New York.
Parol, K. and Rutkowski, A. (1993) Counting the number of isotone selfmappings of crowns,Order 10, 221–226.
Rival, I. and Rutkowski, A. (1991) Does almost every isotone self-map have a fixed point? inExtremal Problems for Finite Sets, Bolyai Soc. Math. Studies,3, Visegrád, Hungary, pp. 413–422.
Rutkowski, A. (1991)On Strictly Increasing Selfmappings of a Fence. How Many of Them Are There? preprint.
Rutkowski, A. (1992) The number of strictly increasing mappings of fences,Order 9, 31–42.
Rutkowski, A. (1992) The formula for the number of order-preserving selfmappings of a fence,Order 9, 127–137.
Stanton, R. G. and Cowan, D. D. (1970) Note on a ‘square’ functional equation,SIAM Review 12, 277–279.
Zaguia, N. (1993) Isotone maps: enumeration and structure, inFinite and Infinite Combinatorics in Sets and Logic, N. W. Sauer, R. E. Woodrow, and B. Sands (eds), Kluwer Academic Publishers, Dordrecht, pp. 421–430.
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Communicated by A. Rutkowski
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Farley, J.D. The number of order-preserving maps between fences and crowns. Order 12, 5–44 (1995). https://doi.org/10.1007/BF01108588
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DOI: https://doi.org/10.1007/BF01108588